Periodic structures are common in natural systems as well as in man made systems. Examples in natural systems are cyclical activity of the biological systems such as the cardio vascular network and the respiratory system. Astronomical systems exhibit periodic phenomena of which the motion of planets is well known. Technological systems are often associated with periodic phenomena, well known are oscillating electronic circuits associated with cyclic transformation of energy and mechanical engines associated with cyclical transformation of chemical to mechanical energy. The analysis of periodicities in systems may provide a key to understanding functional aspects of systems. For example, deviations from the standard cyclical mode can provide insight into the nature of a defect occurring in the system. Thus a malfunctioning valve is a source of a deviation from a standard cyclical pattern of an internal combustion engine. In the medical practice, the correlation existing between the electrical ECG signal and the mechanical cyclical pattern of the heart is a source of information that can be taken to describe the well-being of the cardiac system.
The most prevalent methods for the detection and estimation of periodic phenomena are based on spectral estimation. In general spectral estimation analyses techniques are applied that are equivalent to a Fourier transform of the auto-correlation of the signal. In such an analysis only the instantaneous amplitude of the signal is taken into account. There are cases, however, in which the instantaneous amplitude of the signal does not reveal any clear periodicity, as can be seen in FIGS. 1A-B to which reference is now made. In FIG. 1A a spectrogram of a frequency modulated periodic signal is shown. In FIG. 1B the power spectrum of the spectrogram is shown that does not reveal a periodic structure. In cases where the periodic structures are frequency modulation or amplitude modulations, de-modulation of the signal is necessary before further estimation of periods. The problem becomes more involved in the presence of noise.
For natural signals, periodic structure can be of more subtle nature then plane amplitude or frequency modulation: e.g., the signal may include periodic structures that involve a combination of amplitude and frequency modifications, as well as phase-shifts, in the presence of noise. In other cases, the periodic structure may be composed of modulations (amplitude and/or frequency modulations) of noise, as is the case in some mechanical systems.
There is thus a recognized need for, and it would be highly advantageous to have, a method that allows for reliable estimation of periodic structures in an intricate signal, which will overcome the drawbacks of current methods as described above.